A study looking at the correlation between cholesterol level and distance between home and work found a correlation coefficient of -0.13. How much of the variance in cholesterol level is explained by distance between home and work (i.e., what is the coefficient of determination)?

To determine how much variance in cholesterol level is explained by the distance between home and work, we need to calculate the coefficient of determination, which is obtained by squaring the correlation coefficient.

In this case, the correlation coefficient is -0.13. Squaring this value gives us:

[

(-0.13)^2 = 0.0169

]

To express this in percentage terms, we multiply by 100:

[

0.0169 \times 100 = 1.69%

]

Rounding this value gives us approximately 1.7%. This represents the proportion of variance in cholesterol levels that can be accounted for by the distance between home and work.

Thus, B, which states that 1.7% of the variance in cholesterol level is explained by the distance, is accurate based on the calculated squared correlation coefficient. This statistical concept demonstrates how much one variable can be predicted from another, establishing an understanding of their relationship and its quantitative strength.